#All dependencies in the dependencies.txt file. This should work too
#!pip install numpy pandas IPython seaborn matplotlib folium statsmodels tensorflow scikit-learn

# DATA 
import numpy as np
import pandas as pd

# DASHBOARDS
from IPython.display import HTML

# PLOTTERS
import seaborn as sns
import matplotlib.pyplot as plt

# MAP VISUALIZER
import folium
from folium.plugins import MarkerCluster


# STATISTICS
from statsmodels.tsa.stattools import acf, pacf
from statsmodels.tsa.statespace.sarimax import SARIMAX
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# LSTM
import tensorflow as tf
import tensorflow.keras as keras
from tensorflow.keras.layers import Input, Bidirectional, LSTM, Dense
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split

BASIC Exploratory Data Analysis (EDA)

First Look at The Data

data = pd.read_csv("orders_autumn_2020.csv")
print(data.dtypes)
data.describe()

TIMESTAMP                                                object
ACTUAL_DELIVERY_MINUTES - ESTIMATED_DELIVERY_MINUTES      int64
ITEM_COUNT                                                int64
USER_LAT                                                float64
USER_LONG                                               float64
VENUE_LAT                                               float64
VENUE_LONG                                              float64
ESTIMATED_DELIVERY_MINUTES                                int64
ACTUAL_DELIVERY_MINUTES                                   int64
CLOUD_COVERAGE                                          float64
TEMPERATURE                                             float64
WIND_SPEED                                              float64
PRECIPITATION                                           float64
dtype: object

	ACTUAL_DELIVERY_MINUTES - ESTIMATED_DELIVERY_MINUTES	ITEM_COUNT	USER_LAT	USER_LONG	VENUE_LAT	VENUE_LONG	ESTIMATED_DELIVERY_MINUTES	ACTUAL_DELIVERY_MINUTES	CLOUD_COVERAGE	TEMPERATURE	WIND_SPEED	PRECIPITATION
count	18706.000000	18706.000000	18706.000000	18706.000000	18706.000000	18706.000000	18706.000000	18706.000000	18429.000000	18429.000000	18429.000000	18706.000000
mean	-1.201058	2.688228	60.175234	24.941244	60.175643	24.941214	33.809313	32.608254	11.996853	16.973536	3.790991	0.332756
std	8.979834	1.886455	0.012674	0.016540	0.011509	0.014482	7.340283	10.018879	23.812605	3.411900	1.456017	1.129234
min	-41.000000	1.000000	60.153000	24.909000	60.149000	24.878000	10.000000	6.000000	0.000000	6.100000	0.077419	0.000000
25%	-7.000000	1.000000	60.163000	24.926000	60.167000	24.930000	28.000000	25.000000	0.000000	14.400000	2.696190	0.000000
50%	-2.000000	2.000000	60.175000	24.943000	60.170000	24.941000	33.000000	32.000000	0.000000	16.700000	3.631970	0.000000
75%	5.000000	4.000000	60.186000	24.954000	60.186000	24.950000	38.000000	40.000000	25.000000	18.900000	4.692530	0.000000
max	34.000000	11.000000	60.201000	24.980000	60.219000	25.042000	82.000000	58.000000	100.000000	26.700000	9.857300	6.315790

Spatial View

---

1. We have coordinates. We can visualize the area where the users and venues are located
2. Plotting users and venues locations we find the dataset concerns the city of Helsinki
3. It's hard to tell whether some areas are more populated than others in terms of users and venues. A heatmap could clarify better (below in the Advanced EDA).

---

# Create float columns for convenience, without losing the original ones

data['user_lat'] = pd.to_numeric(data['USER_LAT'])
data['user_lon'] = pd.to_numeric(data['USER_LONG'])
data['venue_lat'] = pd.to_numeric(data['VENUE_LAT'])
data['venue_lon'] = pd.to_numeric(data['VENUE_LONG'])

Venues

#import folium
#from folium.plugins import MarkerCluster


# Create a map centered at Helsinki (blue placeholder)
m = folium.Map(location=[60.1756, 24.9342], zoom_start=13)

# Define Venue Coordinates
coords = zip(data["venue_lat"], data["venue_lon"])

# Use MarkerCluster to group nearby markers
marker_cluster = MarkerCluster().add_to(m)

# Add points to the marker cluster
for coord in coords:
    folium.Marker(location=coord).add_to(marker_cluster)

# Display the map
m

Make this Notebook Trusted to load map: File -> Trust Notebook

Users

#import folium
#from folium.plugins import MarkerCluster


# Create a map centered at Helsinki (blue placeholder)
m = folium.Map(location=[60.1756, 24.9342], zoom_start=13)

# Define Venue Coordinates
coords = zip(data["user_lat"], data["user_lon"])

# Use MarkerCluster to group nearby markers
marker_cluster = MarkerCluster().add_to(m)

# Add points to the marker cluster
for coord in coords:
    folium.Marker(location=coord).add_to(marker_cluster)

# Display the map
m

Make this Notebook Trusted to load map: File -> Trust Notebook

Distributions

---

Three variables carry information about orders' delivery time

1. "ACTUAL_DELIVERY_MINUTES"
2. "ESTIMATED_DELIVERY_MINUTES",
3. "ACTUAL_DELIVERY_MINUTES - ESTIMATED_DELIVERY_MINUTES"

We can look at their single distributions (diagonal). Are they gaussians? Are they skewed?

What's the relation between each variable and the others (scatterplots and kdeplot, off-diagonal)

---

We don't see anything particularly surprising. The (Actual - Estimated Delivery Minutes) variable is gaussian and centered below the 0. Times are calculated so that the user doesn't experience delays, on average.

---

# import seaborn as sns
sub_data = data[["ACTUAL_DELIVERY_MINUTES",
                 "ESTIMATED_DELIVERY_MINUTES",
                 "ACTUAL_DELIVERY_MINUTES - ESTIMATED_DELIVERY_MINUTES"]]
sub_data.columns = ["Actual (Del. Min.)", "Estimated (Del. Min.)", "Act.-Est. (Del. Min.)"]
g = sns.PairGrid(sub_data)
g.map_upper(sns.scatterplot,alpha=0.5, s=10, edgecolor='grey', color = 'pink')
g.map_lower(sns.kdeplot, color = 'pink')
g.map_diag(sns.kdeplot, lw=1, legend=False, color = 'purple')
plt.show()

sub_data.describe()

	Actual (Del. Min.)	Estimated (Del. Min.)	Act.-Est. (Del. Min.)
count	18706.000000	18706.000000	18706.000000
mean	32.608254	33.809313	-1.201058
std	10.018879	7.340283	8.979834
min	6.000000	10.000000	-41.000000
25%	25.000000	28.000000	-7.000000
50%	32.000000	33.000000	-2.000000
75%	40.000000	38.000000	5.000000
max	58.000000	82.000000	34.000000

Time Series

---

We can look for interesting patterns across time. Should we focus on weekly/daily/hourly trends?

Some variables with interesting behaviours could be:

---

1. (Actual - Estimated) Delivery Minutes (Delay)

• Do delays happen more often in certain weekdays/hours of day/day of month?
• What's the time series like for the total window of time in the data? Are there patterns we can predict?

---

1. Number of Orders

• How does the number of orders depend on weekdays/hours of day/day of month?
• What's the time series like for the total window of time in the data? Are there patterns we can predict?

---

1. Other

- Should we expect any relation between time and coordinates or user-venue distance?

# Convert into datetime format
data["Datetime"] = pd.to_datetime(data["TIMESTAMP"])

# Define new dataframe, for convenience
time_df = pd.DataFrame({})
time_df["date"] = data["Datetime"]
time_df["minute"] = data["Datetime"].dt.minute
time_df["hour"] = data["Datetime"].dt.hour
time_df["day"] = data["Datetime"].dt.day
time_df["month"] = data["Datetime"].dt.month
time_df["year"] = data["Datetime"].dt.year


time_df["Delay"] = data["ACTUAL_DELIVERY_MINUTES - ESTIMATED_DELIVERY_MINUTES"]
time_df["Counts"] = len(time_df)*[1]

time_df

	date	minute	hour	day	month	year	Delay	Counts
0	2020-08-01 06:07:00	7	6	1	8	2020	-19	1
1	2020-08-01 06:17:00	17	6	1	8	2020	-7	1
2	2020-08-01 06:54:00	54	6	1	8	2020	-17	1
3	2020-08-01 07:09:00	9	7	1	8	2020	-2	1
4	2020-08-01 07:10:00	10	7	1	8	2020	-1	1
...	...	...	...	...	...	...	...	...
18701	2020-09-30 19:27:00	27	19	30	9	2020	-1	1
18702	2020-09-30 19:36:00	36	19	30	9	2020	-8	1
18703	2020-09-30 19:39:00	39	19	30	9	2020	-14	1
18704	2020-09-30 19:42:00	42	19	30	9	2020	-11	1
18705	2020-09-30 20:04:00	4	20	30	9	2020	-7	1

18706 rows × 8 columns

Delays

def time_series_plotter(granularity = 'day'):
    result_df = time_df.groupby([granularity]).agg({'Delay': 'mean'}).reset_index()
    plt.figure(figsize = (9,3))
    plt.plot(result_df[[granularity]], result_df["Delay"],  linewidth = 0.69, color = 'darkblue',
             marker = '*', markersize = 3.1)
    plt.title(f"Average Delay by {granularity}")
    plt.grid(True, linewidth = 0.3)
    plt.box(False)
    plt.show()

def time_series_plotter_counts(granularity = 'day'):
    result_df = time_df.groupby([granularity]).agg({'Counts': 'sum'}).reset_index()
    plt.figure(figsize = (9,3))
    plt.plot(result_df[[granularity]], result_df["Counts"],  linewidth = 0.69, color = 'darkblue',
             marker = '*', markersize = 3.1)
    plt.title(f"Nr. of Orders by {granularity}")
    plt.grid(True, linewidth = 0.3)
    plt.box(False)
    plt.show()

time_series_plotter('minute')
time_series_plotter('day')
time_series_plotter('hour')

Orders

time_series_plotter_counts('minute')
time_series_plotter_counts('hour')
time_series_plotter_counts('day')

# This is needed for the resampling in the following plots. Set the "date" column as the index

time_df_n = time_df
time_df_n.set_index('date', inplace=True)

Delays

def timeseries_plotter(resampled_by = 'day', indicator = 'mean'):
    dictio = {'minute': 'T','hour': 'H',"day":'D', 'month':'M'}

    # Resample by day and calculate the mean delay for each day
    if indicator == 'mean':
        resampled_df = time_df_n.resample(dictio[resampled_by]).mean()
    elif indicator == 'sum':
        resampled_df = time_df_n.resample(dictio[resampled_by]).sum()
        

    plt.figure(figsize = (9,3))
    # Plot the resampled data
    plt.plot(resampled_df.index, resampled_df['Delay'], linewidth = 0.69, color = 'darkgreen')
    plt.xlabel('Date')
    plt.ylabel('Average Delay')
    plt.suptitle(f'Average Delay Resampled by {resampled_by}')
    plt.title('on total time window', fontsize = 9)
    plt.xticks(rotation = 45)
    plt.grid(True, linewidth = 0.3)
    plt.box(False)
    plt.show()
    
    
#'''
timeseries_plotter('minute')
timeseries_plotter('hour')
timeseries_plotter('day')
'''
timeseries_plotter('minute', indicator = 'sum')
timeseries_plotter('hour', indicator = 'sum')
timeseries_plotter('day', indicator = 'sum')
'''

"\ntimeseries_plotter('minute', indicator = 'sum')\ntimeseries_plotter('hour', indicator = 'sum')\ntimeseries_plotter('day', indicator = 'sum')\n"

Orders

def timeseries_plotter_counts(resampled_by = 'day'):
    dictio = {'minute': 'T','hour': 'H',"day":'D', 'month':'M'}

    # Resample by day and calculate the mean delay for each day
    resampled_df = time_df_n.resample(dictio[resampled_by]).sum()

    plt.figure(figsize = (9,3))
    # Plot the resampled data
    plt.plot(resampled_df.index, resampled_df['Counts'], linewidth = 0.69, color = 'darkgreen')
    plt.xlabel('Date')
    plt.ylabel('Nr. of Orders')
    plt.suptitle(f'Nr. of Orders Resampled by {resampled_by}')
    plt.title('on total time window', fontsize = 9)
    plt.xticks(rotation = 45)
    plt.grid(True, linewidth = 0.3)
    plt.box(False)
    plt.show()
    
timeseries_plotter_counts('minute')
timeseries_plotter_counts('hour')
timeseries_plotter_counts('day')

ADVANCED EDA

Interactive Dashboards

---

Links in case they don't work in the notebook

• EDA 1
• EDA 2
• EDA 3

---

---

Orders and delays time trends

HTML("""
<div class='tableauPlaceholder' id='viz1706449616333' style='position: relative'><noscript><a href='#'><img alt='EDA1 ' src='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;AD&#47;ADVANCEDEDA1&#47;EDA1&#47;1_rss.png' style='border: none' /></a></noscript><object class='tableauViz'  style='display:none;'><param name='host_url' value='https%3A%2F%2Fpublic.tableau.com%2F' /> <param name='embed_code_version' value='3' /> <param name='site_root' value='' /><param name='name' value='ADVANCEDEDA1&#47;EDA1' /><param name='tabs' value='no' /><param name='toolbar' value='yes' /><param name='static_image' value='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;AD&#47;ADVANCEDEDA1&#47;EDA1&#47;1.png' /> <param name='animate_transition' value='yes' /><param name='display_static_image' value='yes' /><param name='display_spinner' value='yes' /><param name='display_overlay' value='yes' /><param name='display_count' value='yes' /><param name='language' value='en-US' /><param name='filter' value='publish=yes' /></object></div>                <script type='text/javascript'>                    var divElement = document.getElementById('viz1706449616333');                    var vizElement = divElement.getElementsByTagName('object')[0];                    if ( divElement.offsetWidth > 800 ) { vizElement.style.width='1000px';vizElement.style.height='827px';} else if ( divElement.offsetWidth > 500 ) { vizElement.style.width='1000px';vizElement.style.height='827px';} else { vizElement.style.width='100%';vizElement.style.height='1477px';}                     var scriptElement = document.createElement('script');                    scriptElement.src = 'https://public.tableau.com/javascripts/api/viz_v1.js';                    vizElement.parentNode.insertBefore(scriptElement, vizElement);                </script>
""")

---

Analysis of Delays (Actual - Estimated Delivery Time > 0)

• Exploring distributions for actual and estimated delivery times, as well as their difference.
• The latter appears to have a gaussian distibution with average lower than zero. Most of the times users don't experience delays
• Are delays linked to specific venues? How are they impacted by venues popularity or location?

HTML("""
<div class='tableauPlaceholder' id='viz1706402227159' style='position: relative'><noscript><a href='#'><img alt='EDA2 ' src='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;AD&#47;ADVANCEDEDA2&#47;EDA2&#47;1_rss.png' style='border: none' /></a></noscript><object class='tableauViz'  style='display:none;'><param name='host_url' value='https%3A%2F%2Fpublic.tableau.com%2F' /> <param name='embed_code_version' value='3' /> <param name='site_root' value='' /><param name='name' value='ADVANCEDEDA2&#47;EDA2' /><param name='tabs' value='no' /><param name='toolbar' value='yes' /><param name='static_image' value='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;AD&#47;ADVANCEDEDA2&#47;EDA2&#47;1.png' /> <param name='animate_transition' value='yes' /><param name='display_static_image' value='yes' /><param name='display_spinner' value='yes' /><param name='display_overlay' value='yes' /><param name='display_count' value='yes' /><param name='language' value='en-US' /><param name='filter' value='publish=yes' /></object></div>                <script type='text/javascript'>                    var divElement = document.getElementById('viz1706402227159');                    var vizElement = divElement.getElementsByTagName('object')[0];                    if ( divElement.offsetWidth > 800 ) { vizElement.style.width='1000px';vizElement.style.height='827px';} else if ( divElement.offsetWidth > 500 ) { vizElement.style.width='1000px';vizElement.style.height='827px';} else { vizElement.style.width='100%';vizElement.style.height='1827px';}                     var scriptElement = document.createElement('script');                    scriptElement.src = 'https://public.tableau.com/javascripts/api/viz_v1.js';                    vizElement.parentNode.insertBefore(scriptElement, vizElement);                </script>
""")

HTML("""
<div class='tableauPlaceholder' id='viz1706464236135' style='position: relative'><noscript><a href='#'><img alt='HeatMap ' src='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;AD&#47;ADVANCEDEDA3&#47;HeatMap&#47;1_rss.png' style='border: none' /></a></noscript><object class='tableauViz'  style='display:none;'><param name='host_url' value='https%3A%2F%2Fpublic.tableau.com%2F' /> <param name='embed_code_version' value='3' /> <param name='site_root' value='' /><param name='name' value='ADVANCEDEDA3&#47;HeatMap' /><param name='tabs' value='no' /><param name='toolbar' value='yes' /><param name='static_image' value='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;AD&#47;ADVANCEDEDA3&#47;HeatMap&#47;1.png' /> <param name='animate_transition' value='yes' /><param name='display_static_image' value='yes' /><param name='display_spinner' value='yes' /><param name='display_overlay' value='yes' /><param name='display_count' value='yes' /><param name='language' value='en-US' /><param name='filter' value='publish=yes' /></object></div>                <script type='text/javascript'>                    var divElement = document.getElementById('viz1706464236135');                    var vizElement = divElement.getElementsByTagName('object')[0];                    if ( divElement.offsetWidth > 800 ) { vizElement.style.width='900px';vizElement.style.height='827px';} else if ( divElement.offsetWidth > 500 ) { vizElement.style.width='900px';vizElement.style.height='827px';} else { vizElement.style.width='100%';vizElement.style.height='1227px';}                     var scriptElement = document.createElement('script');                    scriptElement.src = 'https://public.tableau.com/javascripts/api/viz_v1.js';                    vizElement.parentNode.insertBefore(scriptElement, vizElement);                </script>
""")
    
#"""
#<div class='tableauPlaceholder' id='viz1706401991259' style='position: relative'><noscript><a href='#'><img alt='HeatMap ' src='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;G7&#47;G7DX8ZJ6P&#47;1_rss.png' style='border: none' /></a></noscript><object class='tableauViz'  style='display:none;'><param name='host_url' value='https%3A%2F%2Fpublic.tableau.com%2F' /> <param name='embed_code_version' value='3' /> <param name='path' value='shared&#47;G7DX8ZJ6P' /> <param name='toolbar' value='yes' /><param name='static_image' value='https:&#47;&#47;public.tableau.com&#47;static&#47;images&#47;G7&#47;G7DX8ZJ6P&#47;1.png' /> <param name='animate_transition' value='yes' /><param name='display_static_image' value='yes' /><param name='display_spinner' value='yes' /><param name='display_overlay' value='yes' /><param name='display_count' value='yes' /><param name='language' value='en-US' /></object></div>                <script type='text/javascript'>                    var divElement = document.getElementById('viz1706401991259');                    var vizElement = divElement.getElementsByTagName('object')[0];                    if ( divElement.offsetWidth > 800 ) { vizElement.style.width='900px';vizElement.style.height='827px';} else if ( divElement.offsetWidth > 500 ) { vizElement.style.width='900px';vizElement.style.height='827px';} else { vizElement.style.width='100%';vizElement.style.height='977px';}                     var scriptElement = document.createElement('script');                    scriptElement.src = 'https://public.tableau.com/javascripts/api/viz_v1.js';                    vizElement.parentNode.insertBefore(scriptElement, vizElement);                </script>
#""")

MODEL

---

Some variables are an obvious choice for a prediction task.
For instance, there's no doubt about the benefit and the need of forecasting the number of orders received in a day/hour.

Aim

• The EDA showed some interesting trends/patterns but didn't suggest any unexpected target variable.
  
• The best way to use our data is to predict a well defined variable, the knowledge of which is of obvious utiliy.
  
• We thus focus on the average delay (Actual - Estimated Delivery Minutes).

We try to complete the following task:
PREDICT THE AVERAGE DELAY IN THE NEXT DAY/HOUR

Benefits

This could be helpful for many reasons. For example:

• the company could encourage a higher number of couriers in those day/hours
  where more delays are expected, countering the latter by properly distributing deliveries.
• the app could estimate higher delivery times, in order not to disappoint users.
  In this case users would just be 'conscious' about the longer waiting times.

Approach

• After defining our predictive goal, we will model the time series considering both endogenous and exogenous features.

---

SARIMAX

Seasonal AutoRegressive Integrated Moving Average with Hexogenous features

---

!Remember!

The SARIMAX model is defined by the order parameters (p, d, q) for the ARIMA part and (P, D, Q, s) for the SARIMA part:

• p: The order of the AutoRegressive (AR) part. It represents the number of lags of the dependent variable to be used as predictors.
• d: The degree of differencing. It indicates how many times the data have had past values subtracted to make the series stationary.
• q: The order of the Moving Average (MA) part. It signifies the number of lagged forecast errors that should go into the ARIMA model.
• P: The order of the seasonal part of the AutoRegressive (AR) model.
• D: The degree of seasonal differencing.
• Q: The order of the seasonal part of the Moving Average (MA) model.
• s: The length of the seasonal cycle.

---

1. We can work with daily or hourly delays. We choose hourly time series since we have a good number of samples.

2. We expect periodicity/seasonality. At least we should observe trends on a 24-hours basis

3. We can expect delays to be influenced by hexogenous features, such as weather condition or number of orders.
   -- We rely on preciptations assuming this feature is known in advance when performing the forecast. Weathermen are reliable nowadays :)
   -- We also consider weekday and hour of the day as hexogenous features (for example we know orders are not delivered in certain hours: that is additional information that the model may not completely capture in the naked time series).

---

We will find good orders for the model by looking at the Time Series Autocorrelation and Partial Autocorrelation for different lags.
The presence of 'high' (outside confidence interval) correlation will suggest the parameters for the SARIMAX model.

---

#import pandas as pd
#import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import acf, pacf
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

resampled_df = time_df_n.resample('H').sum()
#resampled_df = time_df_n.resample('D').mean()

def correloplotter(x):
    # Compute the autocorrelation function (ACF)
    acf_vals = x#acf(x)
    pacf_vals = x#pacf(x)


    # Plot the ACF
    plot_acf(acf_vals, lags=30)
    plt.ylim([-1.3,1.3])
    plt.grid(linewidth = 0.1)
    #plt.xticks(range(0,20))
    plt.box(True)
    plt.gca().spines['right'].set_visible(False)
    plt.gca().spines['top'].set_visible(False)
    # Set the width of the axes
    plt.gca().spines['left'].set_linewidth(0.31)
    plt.gca().spines['bottom'].set_linewidth(0.31)

    # Plot the PACF
    plot_pacf(pacf_vals, lags =27)
    plt.ylim([-1.3,1.3])
    plt.grid(linewidth = 0.1)
    plt.box(True)
    plt.gca().spines['right'].set_visible(False)
    plt.gca().spines['top'].set_visible(False)
    # Set the width of the axes
    plt.gca().spines['left'].set_linewidth(0.31)
    plt.gca().spines['bottom'].set_linewidth(0.31)


    plt.show()

correloplotter(resampled_df['Delay'])

C:\Users\diesi\anaconda3\lib\site-packages\statsmodels\graphics\tsaplots.py:348: FutureWarning:

The default method 'yw' can produce PACF values outside of the [-1,1] interval. After 0.13, the default will change tounadjusted Yule-Walker ('ywm'). You can use this method now by setting method='ywm'.

resampled_df['delay_diff'] = resampled_df['Delay'].diff()
resampled_df_dropna = resampled_df.dropna()

correloplotter(resampled_df_dropna['delay_diff'])

C:\Users\diesi\anaconda3\lib\site-packages\statsmodels\graphics\tsaplots.py:348: FutureWarning:

The default method 'yw' can produce PACF values outside of the [-1,1] interval. After 0.13, the default will change tounadjusted Yule-Walker ('ywm'). You can use this method now by setting method='ywm'.

Sarima

# ACF and PACF plots for seasonal component
seasonal_diff = resampled_df['Delay'].diff(24).dropna()

plot_acf(seasonal_diff, lags=10, zero=True)
plt.show()

plot_pacf(seasonal_diff, lags=10, zero=True)
plt.show()

---

Analysis

Let's analyze the findings:

Original Series:

• ACF shows significant spikes at lags 1, 2, 3, 4, 5, 6, and 16 to 27.
• PACF shows significant spikes at lags 1 and 2.

Differencing (non-seasonal):

• ACF after differencing shows significant spikes at lags 1, 6, and 24.
• PACF after differencing shows significant spikes at lags 1, 2, 3, 4, 5, and 16 to 24.

Seasonal Differencing (s=24):

• ACF after seasonal differencing shows significant spikes at lags 1 and 2.
• PACF after seasonal differencing shows significant spikes at lags 1 and 2.

Deductions:

• Considering the ACF and PACF spikes after non-seasonal differencing, it seems there is a seasonal component with a period of 24 hours, as one could expect.

Suggested Orders:

Based on the observations, a SARIMA model may be appropriate. The suggested orders could be as follows:

• Seasonal Order (S): 24 (since the data is hourly and the seasonality is observed every 24 hours).
• Autoregressive Order (p): Consider values around 2 for both the non-seasonal and seasonal components based on the PACF.

• Integrated Order (d): 1 for the non-seasonal component (since differencing at lag 1 shows significance).

• Seasonal Integrated Order (D): 1 for the seasonal component (since seasonal differencing at lag 24 shows significance).

• Moving Average Order (q): Consider values around 2 for both the non-seasonal and seasonal components based on the ACF.

---

Model

---

Dataframe creation. We will have:

• Target Variable ->Average Delay
  Target Variable and time series variable

• Hex. Features -> weekday (number from 1 to 7), hour of the day (1 to 24), Rain (precipitaiotn in mm)
  We could use categorical features but we retain the numerical form

---

Additional considerations:

• order = (2, 1, 2)
• seasonal_order = (2, 1, 2, 24)
• We handle null values (for hours where there are no orders at all) by replacing them with the
  average hourly delay across the whole series (= -1.5)

---

# Define new dataframe, for convenience
time_df = pd.DataFrame({})
time_df["date"] = data["Datetime"]
time_df["minute"] = data["Datetime"].dt.minute
time_df["hour"] = data["Datetime"].dt.hour
time_df["day"] = data["Datetime"].dt.day
time_df["month"] = data["Datetime"].dt.month
time_df["year"] = data["Datetime"].dt.year
time_df["weekday"] = data["Datetime"].dt.weekday


time_df["Delay"] = data["ACTUAL_DELIVERY_MINUTES - ESTIMATED_DELIVERY_MINUTES"]
time_df["Counts"] = len(time_df)*[1]
time_df["Rain"] = data["PRECIPITATION"]

# This is needed for the resampling in the following plots. Set the "date" column as the index
time_df_n = time_df
time_df_n.set_index('date', inplace=True)

# Resample by considering hourly sum of delays
resampled_df = time_df_n.resample('H').sum()
#resampled_df = time_df_n.resample('D').mean()

#print(resampled_df['Delay'].dropna().mean())

for column in resampled_df.columns:
    if column != 'Counts':
        # Perform the division only when "Counts" is not 0, otherwise set the result to 0
        resampled_df[column] = np.where(
            resampled_df["Counts"] != 0, 
            resampled_df[column] / resampled_df["Counts"], -1.5) # or 0)

train_size = int(len(resampled_df) * 0.9)  # 95% for training, 5% for testing
train, test = resampled_df[:train_size], resampled_df[train_size:]

from statsmodels.tsa.statespace.sarimax import SARIMAX

### HOURLY FORECAST ###
order = (2, 1, 2)  # Non-seasonal component
seasonal_order = (2, 1, 2, 24)  # Seasonal component

''''
### DAILY FORECAST ###
order = (2, 1, 1)  # Non-seasonal component
seasonal_order = (2, 1, 2, 7)  # Seasonal component
'''

'''
order = (3, 1, 3)  # Non-seasonal component
seasonal_order = (2, 1, 2, 24)  # Seasonal component
'''

# Fit the SARIMA model
sarima_model = SARIMAX(train['Delay'],
                       order=order,  exog=train[['hour','weekday','Rain']],
                       seasonal_order=seasonal_order,
                       method_kwargs={'maxiter':1000})
fitted_sarima_model = sarima_model.fit()

# Forecast on the test set
sarima_predictions = fitted_sarima_model.get_forecast(len(test), exog=test[['hour','weekday','Rain']])

C:\Users\diesi\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

C:\Users\diesi\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

C:\Users\diesi\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

# Calculate RMSE (Root Mean Squared Error)
rmse = sqrt(mean_squared_error(test['Delay'], sarima_predictions.predicted_mean))
print(f'Root Mean Squared Error (RMSE): {rmse}')

# Plotting the results
plt.figure(figsize=(10, 6))

# Plot training data
plt.plot(train.index, train['Delay'], label='Train', color='gray', linewidth = 0.31)

# Plot actual test data
plt.plot(test.index, test['Delay'], label='Actual', color='green', linewidth = 0.31)

# Plot predicted values
plt.plot(test.index, sarima_predictions.predicted_mean, label='Predicted', color='red', linewidth = 0.31)

# Plot confidence intervals
ci = sarima_predictions.conf_int()
plt.fill_between(test.index, ci['lower Delay'], ci['upper Delay'], color='pink', alpha=0.3, label='Confidence Interval')

plt.title('SARIMA Model: Actual vs. Predicted Values')
plt.xlabel('Date')
plt.ylabel('Delay')
plt.xticks(rotation=45)
plt.legend()
plt.box(True)
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['top'].set_visible(False)
# Set the width of the axes
plt.gca().spines['left'].set_linewidth(0.31)
plt.gca().spines['bottom'].set_linewidth(0.31)
plt.grid(linewidth = 0.1)
plt.show()

##############
### DETAIL ###
##############

# Plotting the results
plt.figure(figsize=(10, 6))

# Plot training data
plt.plot(train.index[-24*3:], train['Delay'][-24*3:], label='Train', color='gray', linewidth = 0.31)

# Plot actual test data
plt.plot(test.index, test['Delay'], label='Actual', color='green', linewidth = 0.31)

# Plot predicted values
plt.plot(test.index, sarima_predictions.predicted_mean, label='Predicted', color='red', linewidth = 0.31)

# Plot confidence intervals
ci = sarima_predictions.conf_int()
plt.fill_between(test.index, ci['lower Delay'], ci['upper Delay'], color='pink', alpha=0.3, label='Confidence Interval')


plt.title('SARIMA Model: Actual vs. Predicted Values (Detail)')
plt.xlabel('Date')
plt.ylabel('Delay')
plt.xticks(rotation=45)
plt.legend()
plt.box(True)
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['top'].set_visible(False)
# Set the width of the axes
plt.gca().spines['left'].set_linewidth(0.31)
plt.gca().spines['bottom'].set_linewidth(0.31)

plt.grid(linewidth = 0.1)
plt.show()

Root Mean Squared Error (RMSE): 2.9221514974542764

---

Diagnostic (below)

Dsitribution

• No trend observed
• No deviation from gaussian distribution, except for a narrower peak of the KDE.

Q-Q Plot:

• The small "s" shape around the diagonal line in the Q-Q plot may indicate slight deviations from normality.
  This is not uncommon at the tails of the distribution.

Correlogram:

• No spikes just outside the confidence band in the correlogram
• The model likely won't benefit from changes in the orders

plt.style.use('bmh') #ggplot')
fitted_sarima_model.plot_diagnostics(figsize=(12, 8))
plt.show()
plt.style.use('default')

---

Results

• The model captures global behaviours and patterns
• High values for hourly delay fail to be predicted, sometimes even trespassing outside of the 95% confidence band.
• RMSE is approx 2.9

---

Deep Learning with LSTMs

Long Short Term Memory Recurrent Neural Networks

Model 1 (Vanilla LSTM)

---

Dataframe creation. We will have:

• Target Variable ->Average Delay. Target Variable and time series variable
  

• Features

  1. weekday (number from 1 to 7), hour of the day (1 to 24), Rain (precipitaiotn in mm)
     We could use categorical features but we retain the numerical form
  2. Past values of the target variable, up to a fixed number (LOOKBACK).
     We set it to 24 but alternative values should be considered

---

Additional considerations:

• 27 features for one target variable. In addition the lstm will be sensitive to sequential patterns
• We handle null values (for hours where there are no orders at all) by replacing them with the
  average hourly delay across the whole series (= -1.5)

---

import tensorflow.keras as keras
from tensorflow.keras.layers import Input, Bidirectional, LSTM, Dense
import tensorflow as tf

from sklearn.metrics import mean_squared_error

# Define new dataframe, for convenience
time_df = pd.DataFrame({})
time_df["date"] = data["Datetime"]
time_df["minute"] = data["Datetime"].dt.minute
time_df["hour"] = data["Datetime"].dt.hour
time_df["day"] = data["Datetime"].dt.day
time_df["month"] = data["Datetime"].dt.month
time_df["year"] = data["Datetime"].dt.year
time_df["weekday"] = data["Datetime"].dt.weekday


time_df["Delay"] = data["ACTUAL_DELIVERY_MINUTES - ESTIMATED_DELIVERY_MINUTES"]
time_df["Counts"] = len(time_df)*[1]
time_df["Rain"] = data["PRECIPITATION"]

# This is needed for the resampling in the following plots. Set the "date" column as the index
time_df_n = time_df
time_df_n.set_index('date', inplace=True)

# Resample by considering hourly sum of delays
resampled_df = time_df_n.resample('H').sum()
#resampled_df = time_df_n.resample('D').mean()

#print(resampled_df['Delay'].dropna().mean())

for column in resampled_df.columns:
    if column != 'Counts':
        # Perform the division only when "Counts" is not 0, otherwise set the result to 0
        resampled_df[column] = np.where(
            resampled_df["Counts"] != 0, 
            resampled_df[column] / resampled_df["Counts"], -1.5) # or 0)

hex_df = resampled_df[['hour','weekday','Rain']]
del_df = resampled_df["Delay"]

# Set the lookback period to 24. This is the number of previous time steps 
# to use as input variables to predict the next time period.
LOOKBACK = 24

# Define a function to wrap the data
def wrap_data(df, lookback):
  # Initialize an empty list to store the dataset
  dataset = []
  
  # Loop over the DataFrame from 'lookback' to the end of the DataFrame
  for index in range(lookback, len(df)+1):
    features = {
        f"col_{i}": float(val) for i, val in enumerate(
          df.iloc[index-lookback:index].values
        )
    }
    
    # Convert the dictionary to a DataFrame and append it to the 'dataset' list
    row = pd.DataFrame.from_dict([features])
    
    # Set the index of the row to be the index of the last period in the lookback window
    row.index = [df.index[index-1]]
    
    # Append the row to the dataset
    dataset.append(row)
  
  # Return a DataFrame obtained by concatenating all the DataFrames in the 'dataset' list
  return pd.concat(dataset, axis=0)

# Obtained features by lagging target variable
dataset = wrap_data(del_df, lookback=LOOKBACK)
# Traget Variable
dataset = dataset.join(del_df.shift(-1))
# Hex. Features
dataset = pd.concat([dataset,hex_df],axis = 1)

dataset = dataset.dropna()

callback = tf.keras.callbacks.EarlyStopping(monitor='loss', patience=3)

def create_model():
    input_layer = Input(shape=(LOOKBACK + len(hex_df.columns), 1))
    recurrent = Bidirectional(LSTM(100, activation="tanh"))(input_layer)
    output_layer = Dense(1)(recurrent)
    model = keras.models.Model(inputs=input_layer, outputs=output_layer)
    model.compile(
        loss='mse', optimizer=keras.optimizers.Adagrad(),
        metrics=[
            keras.metrics.RootMeanSquaredError(),
            keras.metrics.MeanAbsoluteError()
    ])
    return model

model = create_model()

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(
    dataset.drop(columns="Delay"),
    dataset["Delay"],
    shuffle=False, test_size = 0.1)

model.fit(X_train, y_train, epochs=1000, callbacks=[callback])

Epoch 1/1000
41/41 [==============================] - 3s 16ms/step - loss: 10.7438 - root_mean_squared_error: 3.2778 - mean_absolute_error: 2.2524
Epoch 2/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.6810 - root_mean_squared_error: 3.1114 - mean_absolute_error: 1.9822
Epoch 3/1000
41/41 [==============================] - 1s 14ms/step - loss: 9.2782 - root_mean_squared_error: 3.0460 - mean_absolute_error: 1.8392
Epoch 4/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.1602 - root_mean_squared_error: 3.0266 - mean_absolute_error: 1.8040
Epoch 5/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.1281 - root_mean_squared_error: 3.0213 - mean_absolute_error: 1.8053
Epoch 6/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.1179 - root_mean_squared_error: 3.0196 - mean_absolute_error: 1.8082
Epoch 7/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.1098 - root_mean_squared_error: 3.0182 - mean_absolute_error: 1.8056
Epoch 8/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.1030 - root_mean_squared_error: 3.0171 - mean_absolute_error: 1.8041
Epoch 9/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.0964 - root_mean_squared_error: 3.0160 - mean_absolute_error: 1.8019
Epoch 10/1000
41/41 [==============================] - 1s 16ms/step - loss: 9.0915 - root_mean_squared_error: 3.0152 - mean_absolute_error: 1.8046
Epoch 11/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.0844 - root_mean_squared_error: 3.0140 - mean_absolute_error: 1.7959
Epoch 12/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.0816 - root_mean_squared_error: 3.0136 - mean_absolute_error: 1.8027
Epoch 13/1000
41/41 [==============================] - 1s 14ms/step - loss: 9.0766 - root_mean_squared_error: 3.0127 - mean_absolute_error: 1.7968
Epoch 14/1000
41/41 [==============================] - 1s 14ms/step - loss: 9.0719 - root_mean_squared_error: 3.0120 - mean_absolute_error: 1.7925
Epoch 15/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.0686 - root_mean_squared_error: 3.0114 - mean_absolute_error: 1.7939
Epoch 16/1000
41/41 [==============================] - 1s 14ms/step - loss: 9.0641 - root_mean_squared_error: 3.0107 - mean_absolute_error: 1.7914
Epoch 17/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.0588 - root_mean_squared_error: 3.0098 - mean_absolute_error: 1.7914
Epoch 18/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.0564 - root_mean_squared_error: 3.0094 - mean_absolute_error: 1.7905
Epoch 19/1000
41/41 [==============================] - 1s 15ms/step - loss: 9.0528 - root_mean_squared_error: 3.0088 - mean_absolute_error: 1.7907
Epoch 20/1000
41/41 [==============================] - 1s 21ms/step - loss: 9.0473 - root_mean_squared_error: 3.0079 - mean_absolute_error: 1.7892
Epoch 21/1000
41/41 [==============================] - 1s 22ms/step - loss: 9.0450 - root_mean_squared_error: 3.0075 - mean_absolute_error: 1.7889
Epoch 22/1000
41/41 [==============================] - 1s 24ms/step - loss: 9.0414 - root_mean_squared_error: 3.0069 - mean_absolute_error: 1.7905
Epoch 23/1000
41/41 [==============================] - 1s 23ms/step - loss: 9.0390 - root_mean_squared_error: 3.0065 - mean_absolute_error: 1.7881
Epoch 24/1000
41/41 [==============================] - 1s 20ms/step - loss: 9.0367 - root_mean_squared_error: 3.0061 - mean_absolute_error: 1.7862
Epoch 25/1000
41/41 [==============================] - 1s 22ms/step - loss: 9.0328 - root_mean_squared_error: 3.0055 - mean_absolute_error: 1.7861
Epoch 26/1000
41/41 [==============================] - 1s 22ms/step - loss: 9.0315 - root_mean_squared_error: 3.0052 - mean_absolute_error: 1.7851
Epoch 27/1000
41/41 [==============================] - 1s 21ms/step - loss: 9.0250 - root_mean_squared_error: 3.0042 - mean_absolute_error: 1.7815
Epoch 28/1000
41/41 [==============================] - 1s 19ms/step - loss: 9.0229 - root_mean_squared_error: 3.0038 - mean_absolute_error: 1.7843
Epoch 29/1000
41/41 [==============================] - 1s 20ms/step - loss: 9.0201 - root_mean_squared_error: 3.0034 - mean_absolute_error: 1.7834
Epoch 30/1000
41/41 [==============================] - 1s 22ms/step - loss: 9.0170 - root_mean_squared_error: 3.0028 - mean_absolute_error: 1.7823
Epoch 31/1000
41/41 [==============================] - 1s 20ms/step - loss: 9.0142 - root_mean_squared_error: 3.0024 - mean_absolute_error: 1.7845
Epoch 32/1000
41/41 [==============================] - 1s 19ms/step - loss: 9.0133 - root_mean_squared_error: 3.0022 - mean_absolute_error: 1.7805
Epoch 33/1000
41/41 [==============================] - 1s 20ms/step - loss: 9.0098 - root_mean_squared_error: 3.0016 - mean_absolute_error: 1.7791
Epoch 34/1000
41/41 [==============================] - 1s 21ms/step - loss: 9.0070 - root_mean_squared_error: 3.0012 - mean_absolute_error: 1.7797
Epoch 35/1000
41/41 [==============================] - 1s 22ms/step - loss: 9.0053 - root_mean_squared_error: 3.0009 - mean_absolute_error: 1.7754
Epoch 36/1000
41/41 [==============================] - 1s 21ms/step - loss: 9.0022 - root_mean_squared_error: 3.0004 - mean_absolute_error: 1.7763
Epoch 37/1000
41/41 [==============================] - 1s 20ms/step - loss: 9.0003 - root_mean_squared_error: 3.0000 - mean_absolute_error: 1.7750
Epoch 38/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9977 - root_mean_squared_error: 2.9996 - mean_absolute_error: 1.7782
Epoch 39/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9956 - root_mean_squared_error: 2.9993 - mean_absolute_error: 1.7723
Epoch 40/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9935 - root_mean_squared_error: 2.9989 - mean_absolute_error: 1.7757
Epoch 41/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.9909 - root_mean_squared_error: 2.9985 - mean_absolute_error: 1.7761
Epoch 42/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.9903 - root_mean_squared_error: 2.9984 - mean_absolute_error: 1.7746
Epoch 43/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9872 - root_mean_squared_error: 2.9979 - mean_absolute_error: 1.7760
Epoch 44/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.9849 - root_mean_squared_error: 2.9975 - mean_absolute_error: 1.7731
Epoch 45/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9820 - root_mean_squared_error: 2.9970 - mean_absolute_error: 1.7740
Epoch 46/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9804 - root_mean_squared_error: 2.9967 - mean_absolute_error: 1.7715
Epoch 47/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9781 - root_mean_squared_error: 2.9964 - mean_absolute_error: 1.7721
Epoch 48/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.9761 - root_mean_squared_error: 2.9960 - mean_absolute_error: 1.7693
Epoch 49/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9750 - root_mean_squared_error: 2.9958 - mean_absolute_error: 1.7700
Epoch 50/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.9722 - root_mean_squared_error: 2.9954 - mean_absolute_error: 1.7688
Epoch 51/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.9699 - root_mean_squared_error: 2.9950 - mean_absolute_error: 1.7695
Epoch 52/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9674 - root_mean_squared_error: 2.9946 - mean_absolute_error: 1.7684
Epoch 53/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.9676 - root_mean_squared_error: 2.9946 - mean_absolute_error: 1.7684
Epoch 54/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9641 - root_mean_squared_error: 2.9940 - mean_absolute_error: 1.7656
Epoch 55/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.9628 - root_mean_squared_error: 2.9938 - mean_absolute_error: 1.7650
Epoch 56/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.9609 - root_mean_squared_error: 2.9935 - mean_absolute_error: 1.7644
Epoch 57/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9579 - root_mean_squared_error: 2.9930 - mean_absolute_error: 1.7651
Epoch 58/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9572 - root_mean_squared_error: 2.9929 - mean_absolute_error: 1.7626
Epoch 59/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9538 - root_mean_squared_error: 2.9923 - mean_absolute_error: 1.7636
Epoch 60/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9532 - root_mean_squared_error: 2.9922 - mean_absolute_error: 1.7637
Epoch 61/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.9510 - root_mean_squared_error: 2.9918 - mean_absolute_error: 1.7644
Epoch 62/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.9508 - root_mean_squared_error: 2.9918 - mean_absolute_error: 1.7590
Epoch 63/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9487 - root_mean_squared_error: 2.9914 - mean_absolute_error: 1.7578
Epoch 64/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.9473 - root_mean_squared_error: 2.9912 - mean_absolute_error: 1.7583
Epoch 65/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9459 - root_mean_squared_error: 2.9910 - mean_absolute_error: 1.7583
Epoch 66/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9448 - root_mean_squared_error: 2.9908 - mean_absolute_error: 1.7607
Epoch 67/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9433 - root_mean_squared_error: 2.9905 - mean_absolute_error: 1.7575
Epoch 68/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9416 - root_mean_squared_error: 2.9902 - mean_absolute_error: 1.7580
Epoch 69/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9394 - root_mean_squared_error: 2.9899 - mean_absolute_error: 1.7578
Epoch 70/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9383 - root_mean_squared_error: 2.9897 - mean_absolute_error: 1.7586
Epoch 71/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.9364 - root_mean_squared_error: 2.9894 - mean_absolute_error: 1.7571
Epoch 72/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9359 - root_mean_squared_error: 2.9893 - mean_absolute_error: 1.7571
Epoch 73/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9328 - root_mean_squared_error: 2.9888 - mean_absolute_error: 1.7576
Epoch 74/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9316 - root_mean_squared_error: 2.9886 - mean_absolute_error: 1.7553
Epoch 75/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9308 - root_mean_squared_error: 2.9884 - mean_absolute_error: 1.7566
Epoch 76/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9293 - root_mean_squared_error: 2.9882 - mean_absolute_error: 1.7524
Epoch 77/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9287 - root_mean_squared_error: 2.9881 - mean_absolute_error: 1.7551
Epoch 78/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9257 - root_mean_squared_error: 2.9876 - mean_absolute_error: 1.7550
Epoch 79/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9248 - root_mean_squared_error: 2.9874 - mean_absolute_error: 1.7555
Epoch 80/1000
41/41 [==============================] - 1s 24ms/step - loss: 8.9232 - root_mean_squared_error: 2.9872 - mean_absolute_error: 1.7531
Epoch 81/1000
41/41 [==============================] - 1s 26ms/step - loss: 8.9218 - root_mean_squared_error: 2.9869 - mean_absolute_error: 1.7518
Epoch 82/1000
41/41 [==============================] - 1s 25ms/step - loss: 8.9211 - root_mean_squared_error: 2.9868 - mean_absolute_error: 1.7549
Epoch 83/1000
41/41 [==============================] - 1s 25ms/step - loss: 8.9186 - root_mean_squared_error: 2.9864 - mean_absolute_error: 1.7535
Epoch 84/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9179 - root_mean_squared_error: 2.9863 - mean_absolute_error: 1.7514
Epoch 85/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9159 - root_mean_squared_error: 2.9860 - mean_absolute_error: 1.7496
Epoch 86/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9147 - root_mean_squared_error: 2.9858 - mean_absolute_error: 1.7515
Epoch 87/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9140 - root_mean_squared_error: 2.9856 - mean_absolute_error: 1.7476
Epoch 88/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9132 - root_mean_squared_error: 2.9855 - mean_absolute_error: 1.7524
Epoch 89/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9112 - root_mean_squared_error: 2.9852 - mean_absolute_error: 1.7469
Epoch 90/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9103 - root_mean_squared_error: 2.9850 - mean_absolute_error: 1.7510
Epoch 91/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9080 - root_mean_squared_error: 2.9846 - mean_absolute_error: 1.7535
Epoch 92/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9092 - root_mean_squared_error: 2.9848 - mean_absolute_error: 1.7519
Epoch 93/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9064 - root_mean_squared_error: 2.9844 - mean_absolute_error: 1.7518
Epoch 94/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9060 - root_mean_squared_error: 2.9843 - mean_absolute_error: 1.7474
Epoch 95/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.9035 - root_mean_squared_error: 2.9839 - mean_absolute_error: 1.7492
Epoch 96/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9032 - root_mean_squared_error: 2.9838 - mean_absolute_error: 1.7464
Epoch 97/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.9009 - root_mean_squared_error: 2.9834 - mean_absolute_error: 1.7494
Epoch 98/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.8996 - root_mean_squared_error: 2.9832 - mean_absolute_error: 1.7499
Epoch 99/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8987 - root_mean_squared_error: 2.9831 - mean_absolute_error: 1.7458
Epoch 100/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8974 - root_mean_squared_error: 2.9828 - mean_absolute_error: 1.7469
Epoch 101/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8971 - root_mean_squared_error: 2.9828 - mean_absolute_error: 1.7478
Epoch 102/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8955 - root_mean_squared_error: 2.9825 - mean_absolute_error: 1.7461
Epoch 103/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8942 - root_mean_squared_error: 2.9823 - mean_absolute_error: 1.7461
Epoch 104/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8929 - root_mean_squared_error: 2.9821 - mean_absolute_error: 1.7459
Epoch 105/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8926 - root_mean_squared_error: 2.9821 - mean_absolute_error: 1.7470
Epoch 106/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8929 - root_mean_squared_error: 2.9821 - mean_absolute_error: 1.7494
Epoch 107/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8894 - root_mean_squared_error: 2.9815 - mean_absolute_error: 1.7476
Epoch 108/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8888 - root_mean_squared_error: 2.9814 - mean_absolute_error: 1.7442
Epoch 109/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8885 - root_mean_squared_error: 2.9814 - mean_absolute_error: 1.7451
Epoch 110/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8863 - root_mean_squared_error: 2.9810 - mean_absolute_error: 1.7493
Epoch 111/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8866 - root_mean_squared_error: 2.9810 - mean_absolute_error: 1.7475
Epoch 112/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8841 - root_mean_squared_error: 2.9806 - mean_absolute_error: 1.7494
Epoch 113/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8829 - root_mean_squared_error: 2.9804 - mean_absolute_error: 1.7473
Epoch 114/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8829 - root_mean_squared_error: 2.9804 - mean_absolute_error: 1.7415
Epoch 115/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8819 - root_mean_squared_error: 2.9802 - mean_absolute_error: 1.7408
Epoch 116/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8809 - root_mean_squared_error: 2.9801 - mean_absolute_error: 1.7429
Epoch 117/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8796 - root_mean_squared_error: 2.9799 - mean_absolute_error: 1.7457
Epoch 118/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8786 - root_mean_squared_error: 2.9797 - mean_absolute_error: 1.7437
Epoch 119/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8766 - root_mean_squared_error: 2.9794 - mean_absolute_error: 1.7454
Epoch 120/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8758 - root_mean_squared_error: 2.9792 - mean_absolute_error: 1.7423
Epoch 121/1000
41/41 [==============================] - 1s 27ms/step - loss: 8.8759 - root_mean_squared_error: 2.9792 - mean_absolute_error: 1.7423
Epoch 122/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.8742 - root_mean_squared_error: 2.9790 - mean_absolute_error: 1.7393
Epoch 123/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8735 - root_mean_squared_error: 2.9788 - mean_absolute_error: 1.7441
Epoch 124/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8724 - root_mean_squared_error: 2.9787 - mean_absolute_error: 1.7435
Epoch 125/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8715 - root_mean_squared_error: 2.9785 - mean_absolute_error: 1.7415
Epoch 126/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8711 - root_mean_squared_error: 2.9784 - mean_absolute_error: 1.7395
Epoch 127/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8697 - root_mean_squared_error: 2.9782 - mean_absolute_error: 1.7415
Epoch 128/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8691 - root_mean_squared_error: 2.9781 - mean_absolute_error: 1.7419
Epoch 129/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8678 - root_mean_squared_error: 2.9779 - mean_absolute_error: 1.7383
Epoch 130/1000
41/41 [==============================] - 1s 25ms/step - loss: 8.8665 - root_mean_squared_error: 2.9777 - mean_absolute_error: 1.7403
Epoch 131/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8677 - root_mean_squared_error: 2.9779 - mean_absolute_error: 1.7376
Epoch 132/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8653 - root_mean_squared_error: 2.9775 - mean_absolute_error: 1.7366
Epoch 133/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8644 - root_mean_squared_error: 2.9773 - mean_absolute_error: 1.7400
Epoch 134/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8635 - root_mean_squared_error: 2.9772 - mean_absolute_error: 1.7377
Epoch 135/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8623 - root_mean_squared_error: 2.9770 - mean_absolute_error: 1.7380
Epoch 136/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8623 - root_mean_squared_error: 2.9770 - mean_absolute_error: 1.7422
Epoch 137/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.8605 - root_mean_squared_error: 2.9767 - mean_absolute_error: 1.7378
Epoch 138/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.8595 - root_mean_squared_error: 2.9765 - mean_absolute_error: 1.7421
Epoch 139/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8579 - root_mean_squared_error: 2.9762 - mean_absolute_error: 1.7401
Epoch 140/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8584 - root_mean_squared_error: 2.9763 - mean_absolute_error: 1.7426
Epoch 141/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8564 - root_mean_squared_error: 2.9760 - mean_absolute_error: 1.7393
Epoch 142/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8557 - root_mean_squared_error: 2.9759 - mean_absolute_error: 1.7393
Epoch 143/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8554 - root_mean_squared_error: 2.9758 - mean_absolute_error: 1.7365
Epoch 144/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8551 - root_mean_squared_error: 2.9757 - mean_absolute_error: 1.7397
Epoch 145/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8537 - root_mean_squared_error: 2.9755 - mean_absolute_error: 1.7386
Epoch 146/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8539 - root_mean_squared_error: 2.9755 - mean_absolute_error: 1.7357
Epoch 147/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8529 - root_mean_squared_error: 2.9754 - mean_absolute_error: 1.7368
Epoch 148/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8504 - root_mean_squared_error: 2.9750 - mean_absolute_error: 1.7353
Epoch 149/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8506 - root_mean_squared_error: 2.9750 - mean_absolute_error: 1.7359
Epoch 150/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8490 - root_mean_squared_error: 2.9747 - mean_absolute_error: 1.7383
Epoch 151/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8487 - root_mean_squared_error: 2.9747 - mean_absolute_error: 1.7405
Epoch 152/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8478 - root_mean_squared_error: 2.9745 - mean_absolute_error: 1.7342
Epoch 153/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8473 - root_mean_squared_error: 2.9744 - mean_absolute_error: 1.7369
Epoch 154/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8469 - root_mean_squared_error: 2.9744 - mean_absolute_error: 1.7349
Epoch 155/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8456 - root_mean_squared_error: 2.9742 - mean_absolute_error: 1.7390
Epoch 156/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8449 - root_mean_squared_error: 2.9740 - mean_absolute_error: 1.7385
Epoch 157/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8446 - root_mean_squared_error: 2.9740 - mean_absolute_error: 1.7326
Epoch 158/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8432 - root_mean_squared_error: 2.9737 - mean_absolute_error: 1.7322
Epoch 159/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8424 - root_mean_squared_error: 2.9736 - mean_absolute_error: 1.7340
Epoch 160/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8420 - root_mean_squared_error: 2.9736 - mean_absolute_error: 1.7335
Epoch 161/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8419 - root_mean_squared_error: 2.9735 - mean_absolute_error: 1.7315
Epoch 162/1000
41/41 [==============================] - 1s 24ms/step - loss: 8.8399 - root_mean_squared_error: 2.9732 - mean_absolute_error: 1.7320
Epoch 163/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8382 - root_mean_squared_error: 2.9729 - mean_absolute_error: 1.7350
Epoch 164/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8379 - root_mean_squared_error: 2.9729 - mean_absolute_error: 1.7332
Epoch 165/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8370 - root_mean_squared_error: 2.9727 - mean_absolute_error: 1.7382
Epoch 166/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8371 - root_mean_squared_error: 2.9727 - mean_absolute_error: 1.7348
Epoch 167/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8368 - root_mean_squared_error: 2.9727 - mean_absolute_error: 1.7355
Epoch 168/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8349 - root_mean_squared_error: 2.9724 - mean_absolute_error: 1.7360
Epoch 169/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8341 - root_mean_squared_error: 2.9722 - mean_absolute_error: 1.7362
Epoch 170/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8334 - root_mean_squared_error: 2.9721 - mean_absolute_error: 1.7359
Epoch 171/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8324 - root_mean_squared_error: 2.9719 - mean_absolute_error: 1.7381
Epoch 172/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8321 - root_mean_squared_error: 2.9719 - mean_absolute_error: 1.7319
Epoch 173/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8310 - root_mean_squared_error: 2.9717 - mean_absolute_error: 1.7355
Epoch 174/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8317 - root_mean_squared_error: 2.9718 - mean_absolute_error: 1.7357
Epoch 175/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8315 - root_mean_squared_error: 2.9718 - mean_absolute_error: 1.7383
Epoch 176/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8297 - root_mean_squared_error: 2.9715 - mean_absolute_error: 1.7351
Epoch 177/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8289 - root_mean_squared_error: 2.9713 - mean_absolute_error: 1.7364
Epoch 178/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8281 - root_mean_squared_error: 2.9712 - mean_absolute_error: 1.7341
Epoch 179/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8267 - root_mean_squared_error: 2.9710 - mean_absolute_error: 1.7317
Epoch 180/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8257 - root_mean_squared_error: 2.9708 - mean_absolute_error: 1.7360
Epoch 181/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8276 - root_mean_squared_error: 2.9711 - mean_absolute_error: 1.7354
Epoch 182/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8248 - root_mean_squared_error: 2.9707 - mean_absolute_error: 1.7343
Epoch 183/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8250 - root_mean_squared_error: 2.9707 - mean_absolute_error: 1.7337
Epoch 184/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8244 - root_mean_squared_error: 2.9706 - mean_absolute_error: 1.7381
Epoch 185/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8223 - root_mean_squared_error: 2.9702 - mean_absolute_error: 1.7342
Epoch 186/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8228 - root_mean_squared_error: 2.9703 - mean_absolute_error: 1.7300
Epoch 187/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8214 - root_mean_squared_error: 2.9701 - mean_absolute_error: 1.7331
Epoch 188/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8212 - root_mean_squared_error: 2.9701 - mean_absolute_error: 1.7337
Epoch 189/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8206 - root_mean_squared_error: 2.9699 - mean_absolute_error: 1.7319
Epoch 190/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8195 - root_mean_squared_error: 2.9698 - mean_absolute_error: 1.7337
Epoch 191/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8188 - root_mean_squared_error: 2.9697 - mean_absolute_error: 1.7329
Epoch 192/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8181 - root_mean_squared_error: 2.9695 - mean_absolute_error: 1.7310
Epoch 193/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8175 - root_mean_squared_error: 2.9694 - mean_absolute_error: 1.7272
Epoch 194/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8169 - root_mean_squared_error: 2.9693 - mean_absolute_error: 1.7292
Epoch 195/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8164 - root_mean_squared_error: 2.9692 - mean_absolute_error: 1.7296
Epoch 196/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8155 - root_mean_squared_error: 2.9691 - mean_absolute_error: 1.7332
Epoch 197/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8154 - root_mean_squared_error: 2.9691 - mean_absolute_error: 1.7319
Epoch 198/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8134 - root_mean_squared_error: 2.9687 - mean_absolute_error: 1.7324
Epoch 199/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8143 - root_mean_squared_error: 2.9689 - mean_absolute_error: 1.7315
Epoch 200/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8134 - root_mean_squared_error: 2.9687 - mean_absolute_error: 1.7313
Epoch 201/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.8126 - root_mean_squared_error: 2.9686 - mean_absolute_error: 1.7280
Epoch 202/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8109 - root_mean_squared_error: 2.9683 - mean_absolute_error: 1.7302
Epoch 203/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8112 - root_mean_squared_error: 2.9684 - mean_absolute_error: 1.7291
Epoch 204/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8106 - root_mean_squared_error: 2.9683 - mean_absolute_error: 1.7312
Epoch 205/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8104 - root_mean_squared_error: 2.9682 - mean_absolute_error: 1.7311
Epoch 206/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8097 - root_mean_squared_error: 2.9681 - mean_absolute_error: 1.7290
Epoch 207/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8088 - root_mean_squared_error: 2.9680 - mean_absolute_error: 1.7342
Epoch 208/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8079 - root_mean_squared_error: 2.9678 - mean_absolute_error: 1.7308
Epoch 209/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8078 - root_mean_squared_error: 2.9678 - mean_absolute_error: 1.7279
Epoch 210/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8064 - root_mean_squared_error: 2.9676 - mean_absolute_error: 1.7320
Epoch 211/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8065 - root_mean_squared_error: 2.9676 - mean_absolute_error: 1.7249
Epoch 212/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8050 - root_mean_squared_error: 2.9673 - mean_absolute_error: 1.7276
Epoch 213/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8048 - root_mean_squared_error: 2.9673 - mean_absolute_error: 1.7282
Epoch 214/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8040 - root_mean_squared_error: 2.9672 - mean_absolute_error: 1.7298
Epoch 215/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.8034 - root_mean_squared_error: 2.9670 - mean_absolute_error: 1.7278
Epoch 216/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8039 - root_mean_squared_error: 2.9671 - mean_absolute_error: 1.7276
Epoch 217/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8027 - root_mean_squared_error: 2.9669 - mean_absolute_error: 1.7307
Epoch 218/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8026 - root_mean_squared_error: 2.9669 - mean_absolute_error: 1.7309
Epoch 219/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8012 - root_mean_squared_error: 2.9667 - mean_absolute_error: 1.7271
Epoch 220/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.8009 - root_mean_squared_error: 2.9666 - mean_absolute_error: 1.7286
Epoch 221/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7997 - root_mean_squared_error: 2.9664 - mean_absolute_error: 1.7265
Epoch 222/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7992 - root_mean_squared_error: 2.9663 - mean_absolute_error: 1.7258
Epoch 223/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7991 - root_mean_squared_error: 2.9663 - mean_absolute_error: 1.7266
Epoch 224/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7995 - root_mean_squared_error: 2.9664 - mean_absolute_error: 1.7277
Epoch 225/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7983 - root_mean_squared_error: 2.9662 - mean_absolute_error: 1.7262
Epoch 226/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7971 - root_mean_squared_error: 2.9660 - mean_absolute_error: 1.7242
Epoch 227/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7970 - root_mean_squared_error: 2.9660 - mean_absolute_error: 1.7270
Epoch 228/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7959 - root_mean_squared_error: 2.9658 - mean_absolute_error: 1.7290
Epoch 229/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7976 - root_mean_squared_error: 2.9661 - mean_absolute_error: 1.7299
Epoch 230/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7950 - root_mean_squared_error: 2.9656 - mean_absolute_error: 1.7266
Epoch 231/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7948 - root_mean_squared_error: 2.9656 - mean_absolute_error: 1.7270
Epoch 232/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7931 - root_mean_squared_error: 2.9653 - mean_absolute_error: 1.7239
Epoch 233/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7926 - root_mean_squared_error: 2.9652 - mean_absolute_error: 1.7323
Epoch 234/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7924 - root_mean_squared_error: 2.9652 - mean_absolute_error: 1.7294
Epoch 235/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7918 - root_mean_squared_error: 2.9651 - mean_absolute_error: 1.7295
Epoch 236/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7923 - root_mean_squared_error: 2.9652 - mean_absolute_error: 1.7316
Epoch 237/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7917 - root_mean_squared_error: 2.9651 - mean_absolute_error: 1.7278
Epoch 238/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7903 - root_mean_squared_error: 2.9649 - mean_absolute_error: 1.7293
Epoch 239/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7900 - root_mean_squared_error: 2.9648 - mean_absolute_error: 1.7276
Epoch 240/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7884 - root_mean_squared_error: 2.9645 - mean_absolute_error: 1.7296
Epoch 241/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7882 - root_mean_squared_error: 2.9645 - mean_absolute_error: 1.7302
Epoch 242/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7885 - root_mean_squared_error: 2.9645 - mean_absolute_error: 1.7300
Epoch 243/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7869 - root_mean_squared_error: 2.9643 - mean_absolute_error: 1.7246
Epoch 244/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7861 - root_mean_squared_error: 2.9641 - mean_absolute_error: 1.7243
Epoch 245/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7862 - root_mean_squared_error: 2.9642 - mean_absolute_error: 1.7280
Epoch 246/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7857 - root_mean_squared_error: 2.9641 - mean_absolute_error: 1.7243
Epoch 247/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7859 - root_mean_squared_error: 2.9641 - mean_absolute_error: 1.7278
Epoch 248/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7850 - root_mean_squared_error: 2.9640 - mean_absolute_error: 1.7252
Epoch 249/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7845 - root_mean_squared_error: 2.9639 - mean_absolute_error: 1.7258
Epoch 250/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7834 - root_mean_squared_error: 2.9637 - mean_absolute_error: 1.7296
Epoch 251/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7829 - root_mean_squared_error: 2.9636 - mean_absolute_error: 1.7251
Epoch 252/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7821 - root_mean_squared_error: 2.9635 - mean_absolute_error: 1.7239
Epoch 253/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7819 - root_mean_squared_error: 2.9634 - mean_absolute_error: 1.7259
Epoch 254/1000
41/41 [==============================] - 1s 19ms/step - loss: 8.7813 - root_mean_squared_error: 2.9633 - mean_absolute_error: 1.7276
Epoch 255/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7805 - root_mean_squared_error: 2.9632 - mean_absolute_error: 1.7289
Epoch 256/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7805 - root_mean_squared_error: 2.9632 - mean_absolute_error: 1.7235
Epoch 257/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7807 - root_mean_squared_error: 2.9632 - mean_absolute_error: 1.7239
Epoch 258/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7805 - root_mean_squared_error: 2.9632 - mean_absolute_error: 1.7220

<keras.src.callbacks.History at 0x2b28d615300>

def show_result(y_test, predicted):
    plt.figure(figsize=(10, 6))
    plt.plot(y_train.index, y_train, '-', label="Train",  color='gray', linewidth = 0.31)
    plt.plot(y_test.index, y_test, '-', label="actual", color='green', linewidth = 0.31)
    plt.plot(y_test.index, predicted, '-', label="predicted", color='blue', linewidth = 0.31)

    plt.title('LSTM Model: Actual vs. Predicted Values (Detail)')
    plt.xlabel('Date')
    plt.ylabel('Delay')
    plt.legend()
    plt.xticks(rotation=45)
    plt.box(True)
    plt.gca().spines['right'].set_visible(False)
    plt.gca().spines['top'].set_visible(False)
    # Set the width of the axes
    plt.gca().spines['left'].set_linewidth(0.31)
    plt.gca().spines['bottom'].set_linewidth(0.31)
    
    plt.grid(linewidth = 0.1)
    plt.show()

def show_result_detail(y_test, predicted):
    # Plotting the results
    plt.figure(figsize=(10, 6))

    # Plot training data
    #plt.plot(X_train.index[-24*3:], train['Delay'][-24*3:], label='Train', color='gray', linewidth = 0.31)

    plt.plot(y_train.index[-24*3:], y_train[-24*3:], '-', label="Train",  color='gray', linewidth = 0.31)
    plt.plot(y_test.index, y_test, '-', label="actual", color='green', linewidth = 0.31)
    plt.plot(y_test.index, predicted, '-', label="predicted", color='blue', linewidth = 0.31)

    # Plot confidence intervals
    #ci = sarima_predictions.conf_int()
    #plt.fill_between(test.index, ci['lower Delay'], ci['upper Delay'], color='pink', alpha=0.3, label='Confidence Interval')


    plt.title('LSTM Model: Actual vs. Predicted Values (Detail)')
    plt.xlabel('Date')
    plt.ylabel('Delay')
    plt.xticks(rotation=45)
    plt.legend()
    plt.box(True)
    plt.gca().spines['right'].set_visible(False)
    plt.gca().spines['top'].set_visible(False)
    # Set the width of the axes
    plt.gca().spines['left'].set_linewidth(0.31)
    plt.gca().spines['bottom'].set_linewidth(0.31)

    plt.grid(linewidth = 0.1)
    plt.show()
    
    results_df = pd.DataFrame({'test':y_test,'preds':list(predicted)})
    mse = mean_squared_error(results_df.dropna()['test'], results_df.dropna()['preds'])
    rmse = mse**(1/2)
    print(f'Test RMSE: {rmse}')

predicted = model.predict(X_test)
show_result(y_test, predicted)
show_result_detail(y_test, predicted)

5/5 [==============================] - 0s 6ms/step

Test RMSE: 2.8147900311469574

---

Results

• The model captures global behaviours and patterns, but not better than SARIMAX.
• High values for hourly delay fail to be predicted. The predicted values tend to lay around the mean.
• RMSE is approx 2.8

---

Further Developements

• Set different LOOKBACK values
• Upgrade LSTM architecture, add layers and parameters for richer non-linear models.
• Optimize training

---

Model 2 (Multiple Layers LSTM)

• Adding layers to Model 1

def create_complex_model():
    input_layer = Input(shape=(LOOKBACK + len(hex_df.columns), 1))
    
    # Add multiple LSTM layers with dropout
    lstm1 = Bidirectional(LSTM(100, activation="tanh", return_sequences=True))(input_layer)
    lstm1 = Dropout(0.2)(lstm1)
    
    lstm2 = Bidirectional(LSTM(50, activation="tanh", return_sequences=True))(lstm1)
    lstm2 = Dropout(0.2)(lstm2)
    
    lstm3 = Bidirectional(LSTM(25, activation="tanh"))(lstm2)
    lstm3 = Dropout(0.2)(lstm3)
    
    # Concatenate the output of the last LSTM layer with the input for skip connections
    #concat_layer = Concatenate()([lstm3, input_layer])
    
    # Dense layers for final prediction
    dense1 = Dense(50, activation='relu')(lstm3)
    #dense1 = Dense(50, activation='relu')(concat_layer)
    dense1 = Dropout(0.2)(dense1)
    
    dense2 = Dense(25, activation='relu')(dense1)
    dense2 = Dropout(0.2)(dense2)
    
    output_layer = Dense(1)(dense2)
    
    model = keras.models.Model(inputs=input_layer, outputs=output_layer)
    
    model.compile(
        loss='mse',
        optimizer=keras.optimizers.Adam(),
        metrics=[
            keras.metrics.RootMeanSquaredError(),
            keras.metrics.MeanAbsoluteError()
        ]
    )
    
    return model

model.fit(X_train, y_train, epochs=1000, callbacks=[callback])

Epoch 1/1000
41/41 [==============================] - 1s 15ms/step - loss: 8.7798 - root_mean_squared_error: 2.9631 - mean_absolute_error: 1.7224
Epoch 2/1000
41/41 [==============================] - 1s 15ms/step - loss: 8.7784 - root_mean_squared_error: 2.9628 - mean_absolute_error: 1.7238
Epoch 3/1000
41/41 [==============================] - 1s 15ms/step - loss: 8.7787 - root_mean_squared_error: 2.9629 - mean_absolute_error: 1.7257
Epoch 4/1000
41/41 [==============================] - 1s 15ms/step - loss: 8.7776 - root_mean_squared_error: 2.9627 - mean_absolute_error: 1.7268
Epoch 5/1000
41/41 [==============================] - 1s 16ms/step - loss: 8.7783 - root_mean_squared_error: 2.9628 - mean_absolute_error: 1.7249
Epoch 6/1000
41/41 [==============================] - 1s 15ms/step - loss: 8.7778 - root_mean_squared_error: 2.9627 - mean_absolute_error: 1.7271
Epoch 7/1000
41/41 [==============================] - 1s 14ms/step - loss: 8.7757 - root_mean_squared_error: 2.9624 - mean_absolute_error: 1.7229
Epoch 8/1000
41/41 [==============================] - 1s 16ms/step - loss: 8.7759 - root_mean_squared_error: 2.9624 - mean_absolute_error: 1.7238
Epoch 9/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7762 - root_mean_squared_error: 2.9625 - mean_absolute_error: 1.7264
Epoch 10/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7736 - root_mean_squared_error: 2.9620 - mean_absolute_error: 1.7204
Epoch 11/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7733 - root_mean_squared_error: 2.9620 - mean_absolute_error: 1.7220
Epoch 12/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7733 - root_mean_squared_error: 2.9620 - mean_absolute_error: 1.7259
Epoch 13/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7734 - root_mean_squared_error: 2.9620 - mean_absolute_error: 1.7270
Epoch 14/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7727 - root_mean_squared_error: 2.9619 - mean_absolute_error: 1.7230
Epoch 15/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7716 - root_mean_squared_error: 2.9617 - mean_absolute_error: 1.7251
Epoch 16/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7702 - root_mean_squared_error: 2.9615 - mean_absolute_error: 1.7291
Epoch 17/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7697 - root_mean_squared_error: 2.9614 - mean_absolute_error: 1.7266
Epoch 18/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7696 - root_mean_squared_error: 2.9614 - mean_absolute_error: 1.7219
Epoch 19/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7691 - root_mean_squared_error: 2.9613 - mean_absolute_error: 1.7240
Epoch 20/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7692 - root_mean_squared_error: 2.9613 - mean_absolute_error: 1.7205
Epoch 21/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7683 - root_mean_squared_error: 2.9611 - mean_absolute_error: 1.7222
Epoch 22/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7677 - root_mean_squared_error: 2.9610 - mean_absolute_error: 1.7203
Epoch 23/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7675 - root_mean_squared_error: 2.9610 - mean_absolute_error: 1.7207
Epoch 24/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7673 - root_mean_squared_error: 2.9610 - mean_absolute_error: 1.7236
Epoch 25/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7664 - root_mean_squared_error: 2.9608 - mean_absolute_error: 1.7233
Epoch 26/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7653 - root_mean_squared_error: 2.9606 - mean_absolute_error: 1.7225
Epoch 27/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7661 - root_mean_squared_error: 2.9608 - mean_absolute_error: 1.7265
Epoch 28/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7647 - root_mean_squared_error: 2.9605 - mean_absolute_error: 1.7254
Epoch 29/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7646 - root_mean_squared_error: 2.9605 - mean_absolute_error: 1.7255
Epoch 30/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.7639 - root_mean_squared_error: 2.9604 - mean_absolute_error: 1.7193
Epoch 31/1000
41/41 [==============================] - 1s 24ms/step - loss: 8.7633 - root_mean_squared_error: 2.9603 - mean_absolute_error: 1.7220
Epoch 32/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7629 - root_mean_squared_error: 2.9602 - mean_absolute_error: 1.7213
Epoch 33/1000
41/41 [==============================] - 1s 26ms/step - loss: 8.7634 - root_mean_squared_error: 2.9603 - mean_absolute_error: 1.7240
Epoch 34/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7620 - root_mean_squared_error: 2.9601 - mean_absolute_error: 1.7220
Epoch 35/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7616 - root_mean_squared_error: 2.9600 - mean_absolute_error: 1.7246
Epoch 36/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7619 - root_mean_squared_error: 2.9601 - mean_absolute_error: 1.7227
Epoch 37/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7604 - root_mean_squared_error: 2.9598 - mean_absolute_error: 1.7222
Epoch 38/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7608 - root_mean_squared_error: 2.9599 - mean_absolute_error: 1.7229
Epoch 39/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7595 - root_mean_squared_error: 2.9596 - mean_absolute_error: 1.7239
Epoch 40/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7596 - root_mean_squared_error: 2.9597 - mean_absolute_error: 1.7261
Epoch 41/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.7589 - root_mean_squared_error: 2.9595 - mean_absolute_error: 1.7226
Epoch 42/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7588 - root_mean_squared_error: 2.9595 - mean_absolute_error: 1.7263
Epoch 43/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7578 - root_mean_squared_error: 2.9594 - mean_absolute_error: 1.7218
Epoch 44/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7576 - root_mean_squared_error: 2.9593 - mean_absolute_error: 1.7211
Epoch 45/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7568 - root_mean_squared_error: 2.9592 - mean_absolute_error: 1.7206
Epoch 46/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7567 - root_mean_squared_error: 2.9592 - mean_absolute_error: 1.7182
Epoch 47/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7564 - root_mean_squared_error: 2.9591 - mean_absolute_error: 1.7211
Epoch 48/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7561 - root_mean_squared_error: 2.9591 - mean_absolute_error: 1.7194
Epoch 49/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7551 - root_mean_squared_error: 2.9589 - mean_absolute_error: 1.7232
Epoch 50/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7539 - root_mean_squared_error: 2.9587 - mean_absolute_error: 1.7222
Epoch 51/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7540 - root_mean_squared_error: 2.9587 - mean_absolute_error: 1.7204
Epoch 52/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7536 - root_mean_squared_error: 2.9586 - mean_absolute_error: 1.7203
Epoch 53/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7523 - root_mean_squared_error: 2.9584 - mean_absolute_error: 1.7160
Epoch 54/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7522 - root_mean_squared_error: 2.9584 - mean_absolute_error: 1.7231
Epoch 55/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7527 - root_mean_squared_error: 2.9585 - mean_absolute_error: 1.7215
Epoch 56/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7515 - root_mean_squared_error: 2.9583 - mean_absolute_error: 1.7167
Epoch 57/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7524 - root_mean_squared_error: 2.9584 - mean_absolute_error: 1.7225
Epoch 58/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7504 - root_mean_squared_error: 2.9581 - mean_absolute_error: 1.7219
Epoch 59/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7500 - root_mean_squared_error: 2.9580 - mean_absolute_error: 1.7207
Epoch 60/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7493 - root_mean_squared_error: 2.9579 - mean_absolute_error: 1.7217
Epoch 61/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7497 - root_mean_squared_error: 2.9580 - mean_absolute_error: 1.7215
Epoch 62/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7480 - root_mean_squared_error: 2.9577 - mean_absolute_error: 1.7216
Epoch 63/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7484 - root_mean_squared_error: 2.9578 - mean_absolute_error: 1.7212
Epoch 64/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7466 - root_mean_squared_error: 2.9575 - mean_absolute_error: 1.7215
Epoch 65/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7465 - root_mean_squared_error: 2.9574 - mean_absolute_error: 1.7194
Epoch 66/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7473 - root_mean_squared_error: 2.9576 - mean_absolute_error: 1.7211
Epoch 67/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7457 - root_mean_squared_error: 2.9573 - mean_absolute_error: 1.7227
Epoch 68/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7462 - root_mean_squared_error: 2.9574 - mean_absolute_error: 1.7220
Epoch 69/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7453 - root_mean_squared_error: 2.9573 - mean_absolute_error: 1.7170
Epoch 70/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7449 - root_mean_squared_error: 2.9572 - mean_absolute_error: 1.7196
Epoch 71/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7431 - root_mean_squared_error: 2.9569 - mean_absolute_error: 1.7164
Epoch 72/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7432 - root_mean_squared_error: 2.9569 - mean_absolute_error: 1.7244
Epoch 73/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7436 - root_mean_squared_error: 2.9570 - mean_absolute_error: 1.7218
Epoch 74/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7426 - root_mean_squared_error: 2.9568 - mean_absolute_error: 1.7226
Epoch 75/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7429 - root_mean_squared_error: 2.9568 - mean_absolute_error: 1.7213
Epoch 76/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7416 - root_mean_squared_error: 2.9566 - mean_absolute_error: 1.7178
Epoch 77/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7401 - root_mean_squared_error: 2.9564 - mean_absolute_error: 1.7186
Epoch 78/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7400 - root_mean_squared_error: 2.9563 - mean_absolute_error: 1.7198
Epoch 79/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7408 - root_mean_squared_error: 2.9565 - mean_absolute_error: 1.7195
Epoch 80/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7390 - root_mean_squared_error: 2.9562 - mean_absolute_error: 1.7235
Epoch 81/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7381 - root_mean_squared_error: 2.9560 - mean_absolute_error: 1.7227
Epoch 82/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7382 - root_mean_squared_error: 2.9560 - mean_absolute_error: 1.7165
Epoch 83/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7380 - root_mean_squared_error: 2.9560 - mean_absolute_error: 1.7208
Epoch 84/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7378 - root_mean_squared_error: 2.9560 - mean_absolute_error: 1.7161
Epoch 85/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7371 - root_mean_squared_error: 2.9559 - mean_absolute_error: 1.7225
Epoch 86/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7368 - root_mean_squared_error: 2.9558 - mean_absolute_error: 1.7198
Epoch 87/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7370 - root_mean_squared_error: 2.9558 - mean_absolute_error: 1.7189
Epoch 88/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7358 - root_mean_squared_error: 2.9556 - mean_absolute_error: 1.7188
Epoch 89/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.7351 - root_mean_squared_error: 2.9555 - mean_absolute_error: 1.7182
Epoch 90/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7354 - root_mean_squared_error: 2.9556 - mean_absolute_error: 1.7201
Epoch 91/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7344 - root_mean_squared_error: 2.9554 - mean_absolute_error: 1.7176
Epoch 92/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7349 - root_mean_squared_error: 2.9555 - mean_absolute_error: 1.7196
Epoch 93/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7350 - root_mean_squared_error: 2.9555 - mean_absolute_error: 1.7205
Epoch 94/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7336 - root_mean_squared_error: 2.9553 - mean_absolute_error: 1.7182
Epoch 95/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7343 - root_mean_squared_error: 2.9554 - mean_absolute_error: 1.7170
Epoch 96/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7338 - root_mean_squared_error: 2.9553 - mean_absolute_error: 1.7158
Epoch 97/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7314 - root_mean_squared_error: 2.9549 - mean_absolute_error: 1.7140
Epoch 98/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7311 - root_mean_squared_error: 2.9548 - mean_absolute_error: 1.7193
Epoch 99/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7307 - root_mean_squared_error: 2.9548 - mean_absolute_error: 1.7173
Epoch 100/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7307 - root_mean_squared_error: 2.9548 - mean_absolute_error: 1.7167
Epoch 101/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7306 - root_mean_squared_error: 2.9548 - mean_absolute_error: 1.7172
Epoch 102/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7300 - root_mean_squared_error: 2.9547 - mean_absolute_error: 1.7177
Epoch 103/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7291 - root_mean_squared_error: 2.9545 - mean_absolute_error: 1.7177
Epoch 104/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7296 - root_mean_squared_error: 2.9546 - mean_absolute_error: 1.7127
Epoch 105/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7289 - root_mean_squared_error: 2.9545 - mean_absolute_error: 1.7140
Epoch 106/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7281 - root_mean_squared_error: 2.9543 - mean_absolute_error: 1.7183
Epoch 107/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7281 - root_mean_squared_error: 2.9543 - mean_absolute_error: 1.7176
Epoch 108/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7276 - root_mean_squared_error: 2.9543 - mean_absolute_error: 1.7169
Epoch 109/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7269 - root_mean_squared_error: 2.9541 - mean_absolute_error: 1.7159
Epoch 110/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7259 - root_mean_squared_error: 2.9540 - mean_absolute_error: 1.7159
Epoch 111/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7262 - root_mean_squared_error: 2.9540 - mean_absolute_error: 1.7167
Epoch 112/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7256 - root_mean_squared_error: 2.9539 - mean_absolute_error: 1.7181
Epoch 113/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7244 - root_mean_squared_error: 2.9537 - mean_absolute_error: 1.7174
Epoch 114/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7239 - root_mean_squared_error: 2.9536 - mean_absolute_error: 1.7184
Epoch 115/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7245 - root_mean_squared_error: 2.9537 - mean_absolute_error: 1.7192
Epoch 116/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7236 - root_mean_squared_error: 2.9536 - mean_absolute_error: 1.7180
Epoch 117/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7236 - root_mean_squared_error: 2.9536 - mean_absolute_error: 1.7150
Epoch 118/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7228 - root_mean_squared_error: 2.9534 - mean_absolute_error: 1.7195
Epoch 119/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7226 - root_mean_squared_error: 2.9534 - mean_absolute_error: 1.7176
Epoch 120/1000
41/41 [==============================] - 1s 24ms/step - loss: 8.7222 - root_mean_squared_error: 2.9533 - mean_absolute_error: 1.7168
Epoch 121/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7216 - root_mean_squared_error: 2.9532 - mean_absolute_error: 1.7218
Epoch 122/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7214 - root_mean_squared_error: 2.9532 - mean_absolute_error: 1.7206
Epoch 123/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7210 - root_mean_squared_error: 2.9531 - mean_absolute_error: 1.7180
Epoch 124/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7208 - root_mean_squared_error: 2.9531 - mean_absolute_error: 1.7166
Epoch 125/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7203 - root_mean_squared_error: 2.9530 - mean_absolute_error: 1.7158
Epoch 126/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7193 - root_mean_squared_error: 2.9528 - mean_absolute_error: 1.7205
Epoch 127/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7195 - root_mean_squared_error: 2.9529 - mean_absolute_error: 1.7157
Epoch 128/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7195 - root_mean_squared_error: 2.9529 - mean_absolute_error: 1.7178
Epoch 129/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7189 - root_mean_squared_error: 2.9528 - mean_absolute_error: 1.7144
Epoch 130/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7175 - root_mean_squared_error: 2.9525 - mean_absolute_error: 1.7124
Epoch 131/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7176 - root_mean_squared_error: 2.9526 - mean_absolute_error: 1.7201
Epoch 132/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7157 - root_mean_squared_error: 2.9522 - mean_absolute_error: 1.7178
Epoch 133/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7170 - root_mean_squared_error: 2.9525 - mean_absolute_error: 1.7182
Epoch 134/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7153 - root_mean_squared_error: 2.9522 - mean_absolute_error: 1.7151
Epoch 135/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7156 - root_mean_squared_error: 2.9522 - mean_absolute_error: 1.7168
Epoch 136/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7146 - root_mean_squared_error: 2.9521 - mean_absolute_error: 1.7162
Epoch 137/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7141 - root_mean_squared_error: 2.9520 - mean_absolute_error: 1.7182
Epoch 138/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7141 - root_mean_squared_error: 2.9520 - mean_absolute_error: 1.7173
Epoch 139/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7151 - root_mean_squared_error: 2.9521 - mean_absolute_error: 1.7205
Epoch 140/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7145 - root_mean_squared_error: 2.9520 - mean_absolute_error: 1.7167
Epoch 141/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7131 - root_mean_squared_error: 2.9518 - mean_absolute_error: 1.7191
Epoch 142/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7118 - root_mean_squared_error: 2.9516 - mean_absolute_error: 1.7203
Epoch 143/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7118 - root_mean_squared_error: 2.9516 - mean_absolute_error: 1.7174
Epoch 144/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7116 - root_mean_squared_error: 2.9515 - mean_absolute_error: 1.7148
Epoch 145/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7117 - root_mean_squared_error: 2.9516 - mean_absolute_error: 1.7201
Epoch 146/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7098 - root_mean_squared_error: 2.9512 - mean_absolute_error: 1.7177
Epoch 147/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7107 - root_mean_squared_error: 2.9514 - mean_absolute_error: 1.7162
Epoch 148/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7087 - root_mean_squared_error: 2.9510 - mean_absolute_error: 1.7201
Epoch 149/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7090 - root_mean_squared_error: 2.9511 - mean_absolute_error: 1.7169
Epoch 150/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7083 - root_mean_squared_error: 2.9510 - mean_absolute_error: 1.7168
Epoch 151/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7076 - root_mean_squared_error: 2.9509 - mean_absolute_error: 1.7207
Epoch 152/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7087 - root_mean_squared_error: 2.9510 - mean_absolute_error: 1.7174
Epoch 153/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7072 - root_mean_squared_error: 2.9508 - mean_absolute_error: 1.7183
Epoch 154/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7066 - root_mean_squared_error: 2.9507 - mean_absolute_error: 1.7149
Epoch 155/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7076 - root_mean_squared_error: 2.9509 - mean_absolute_error: 1.7169
Epoch 156/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7055 - root_mean_squared_error: 2.9505 - mean_absolute_error: 1.7147
Epoch 157/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7058 - root_mean_squared_error: 2.9506 - mean_absolute_error: 1.7158
Epoch 158/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7049 - root_mean_squared_error: 2.9504 - mean_absolute_error: 1.7144
Epoch 159/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7051 - root_mean_squared_error: 2.9504 - mean_absolute_error: 1.7133
Epoch 160/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7038 - root_mean_squared_error: 2.9502 - mean_absolute_error: 1.7137
Epoch 161/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7042 - root_mean_squared_error: 2.9503 - mean_absolute_error: 1.7184
Epoch 162/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.7033 - root_mean_squared_error: 2.9501 - mean_absolute_error: 1.7134
Epoch 163/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7026 - root_mean_squared_error: 2.9500 - mean_absolute_error: 1.7105
Epoch 164/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7019 - root_mean_squared_error: 2.9499 - mean_absolute_error: 1.7130
Epoch 165/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.7027 - root_mean_squared_error: 2.9500 - mean_absolute_error: 1.7141
Epoch 166/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.7011 - root_mean_squared_error: 2.9498 - mean_absolute_error: 1.7159
Epoch 167/1000
41/41 [==============================] - 1s 25ms/step - loss: 8.7002 - root_mean_squared_error: 2.9496 - mean_absolute_error: 1.7149
Epoch 168/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.7005 - root_mean_squared_error: 2.9497 - mean_absolute_error: 1.7151
Epoch 169/1000
41/41 [==============================] - 1s 28ms/step - loss: 8.6993 - root_mean_squared_error: 2.9495 - mean_absolute_error: 1.7150
Epoch 170/1000
41/41 [==============================] - 1s 24ms/step - loss: 8.7009 - root_mean_squared_error: 2.9497 - mean_absolute_error: 1.7174
Epoch 171/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.6999 - root_mean_squared_error: 2.9496 - mean_absolute_error: 1.7172
Epoch 172/1000
41/41 [==============================] - 1s 27ms/step - loss: 8.6989 - root_mean_squared_error: 2.9494 - mean_absolute_error: 1.7146
Epoch 173/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.6982 - root_mean_squared_error: 2.9493 - mean_absolute_error: 1.7169
Epoch 174/1000
41/41 [==============================] - 1s 22ms/step - loss: 8.6982 - root_mean_squared_error: 2.9493 - mean_absolute_error: 1.7164
Epoch 175/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.6970 - root_mean_squared_error: 2.9491 - mean_absolute_error: 1.7144
Epoch 176/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.6972 - root_mean_squared_error: 2.9491 - mean_absolute_error: 1.7153
Epoch 177/1000
41/41 [==============================] - 1s 20ms/step - loss: 8.6967 - root_mean_squared_error: 2.9490 - mean_absolute_error: 1.7152
Epoch 178/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.6951 - root_mean_squared_error: 2.9487 - mean_absolute_error: 1.7182
Epoch 179/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.6965 - root_mean_squared_error: 2.9490 - mean_absolute_error: 1.7142
Epoch 180/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.6941 - root_mean_squared_error: 2.9486 - mean_absolute_error: 1.7163
Epoch 181/1000
41/41 [==============================] - 1s 23ms/step - loss: 8.6942 - root_mean_squared_error: 2.9486 - mean_absolute_error: 1.7170
Epoch 182/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.6959 - root_mean_squared_error: 2.9489 - mean_absolute_error: 1.7134
Epoch 183/1000
41/41 [==============================] - 1s 21ms/step - loss: 8.6943 - root_mean_squared_error: 2.9486 - mean_absolute_error: 1.7125

<keras.src.callbacks.History at 0x2b2c266c7c0>

predicted = model.predict(X_test)
show_result(y_test, predicted)
show_result_detail(y_test, predicted)

5/5 [==============================] - 0s 9ms/step

Test RMSE: 2.797925942229235

---

Results

• The model captures global behaviours and patterns, but not better than SARIMAX.
• High values for hourly delay fail to be predicted. The predicted values tend to lay around the mean.
• RMSE is approx 2.8

---

Further Developements

• Set different LOOKBACK values
• Upgrade LSTM architecture, add layers and parameters for richer non-linear models.
• Optimize training

---

CONCLUSIONS AND FURTHER DEVELOPMENTS

• Forecasting daily delays rather than hourly ones would be reasonable, and likely yield better results.
  More data is needed in order to do that.
• SARIMAX and LSTM models should be optimized by tuning parameters and modifying architectures.
• Anomaly detection could be employed to predict spikes in the delivery time.
• More advanced models should be considered. LSTMs could be replaced by Transformers.

#!pip freeze